This formula is in apparent contradiction with what we saw in the
analysis of the gravitational waves in GR, where the unique sort
of the propagating degrees of freedom are the tensor (transverse and
traceless) modes. The explanation of this apparent discrepancy is
that the smooth \(\,\Psi \rightarrow 0\,\)  limit in (REF )
corresponds to the theory after the Faddeev-Popov procedure,
which extends the space of the propagating modes and make the
whole propagator non-degenerate. On the contrary, the result for
the gravitational waves is based on another procedure, i.e.,
removing all degrees of freedom by using gauge transformation
and its remnant (see, e.g., [1]}).
